Question

A doctor is measuring the mean systolic blood pressure of female students at a large college. Systolic blood pressure is known to have a skewed distribution. The doctor collects systolic blood pressure measurements from random sample of 28 female students. The resulting 90% confidence interval is (100. 4, 159. 6). Units of systolic blood pressure are mmhg. Which one of the following conclusions is valid?

Answer 1

Using the Central Limit Theorem, it is found that the valid conclusion is given as follows:

The sampling distribution will probably not follow a normal distribution, hence we cannot draw a conclusion.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have a skewed variable with a sample size less than 30, hence the Central Limit Theorem cannot be applied and the correct conclusion is:

The sampling distribution will probably not follow a normal distribution, hence we cannot draw a conclusion.

To learn more about the Central Limit Theorem, you can check brainly.com/question/24663213